Calculating Electrostatic Pressure on a Charged Sphere

In summary, the sphere is charged with surface density σ, and the electrostatic pressure is equal to 1/2*sigma*delta s.
  • #1
springo
126
0

Homework Statement


A sphere with radius R is charged with surface density σ. The charge found in a small surface Δs is repelled by the rest of the sphere, thus generating an electrostatic pressure. Find the pressure.

Homework Equations



The Attempt at a Solution


I think I have to compute the field for the sphere, which can be done using Gauss' law. For Δs: Esph = σ/ε0
Then I think I have to find the field for Δs and subtract it, but I don't know how to find it.
If field is constant, ten just multiplying QΔs = Δs·σ by the field would give the force.

Thanks for your help!
 
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  • #2
springo said:
1.
If field is constant, ten just multiplying QΔs = Δs·σ by the field would give the force.

Yes. And force per unit area will be pressure.
 
  • #3
rl.bhat said:
Yes. And force per unit area will be pressure.
Thanks.

Now how do I find the field for Δs?
 
  • #4
The magnitude of the electric field at every point on the sphere is the same and is equal to Esph = σ/ε0
 
  • #5
rl.bhat said:
The magnitude of the electric field at every point on the sphere is the same and is equal to Esph = σ/ε0
Yes, but I what meant to is: shouldn't I find the field generated by the sphere and subtract the field generated by Δs to have the field generated by a sphere without Δs? If so, my problem is that I don't know how to find the field generated by Δs.
 
  • #6
Bump...
 
  • #7
A body does not exert force on its own surface. So if you want to find pressure on delta s,
assume that it is removed from the sphere and kept very close to the sphere. When you remove delta s from the sphere, charge on each surface of delta s will be 1/2*sigma*delta s. Since delta s is very small, field due sphere close to its surface does no change much. So it will be sigma/ epsilon(not). So the pressure =force /area = 1/2*sigma*delta s*sigma/epsilon(not) = (sigma)^2/2epsilon(not)
 
  • #8
OK thanks, I understand now. Just one small thing, why is the charge 1/2·Δs·σ? I thought the charge equals to surface (Δs) multiplied by the density (σ). Where does the 1/2 come from?
 
  • #9
When the delta s is on the sphere , charge sigma delta s is only on outer surface. When you remove it from the sphere, charge distributes equally on both the surfaces. Hence 1/2*sigma*delta s.
 
  • #10
OK thanks!
 

1. What is electrostatic pressure?

Electrostatic pressure refers to the force exerted between two electrically charged objects or particles. It is caused by the repulsion or attraction of positive and negative charges.

2. How is electrostatic pressure calculated?

Electrostatic pressure can be calculated using Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. What are some real-life examples of electrostatic pressure?

Some common examples of electrostatic pressure include the spark that occurs when you touch a metal doorknob after walking on carpet, the force that causes a balloon to stick to a wall after rubbing it on your hair, and the attraction between clothes in a dryer due to static electricity.

4. How does electrostatic pressure differ from other types of pressure?

Unlike other types of pressure, such as air or water pressure, electrostatic pressure is caused by the interaction of electric charges and does not require the presence of physical matter. It also follows different mathematical equations and can be attractive or repulsive, depending on the charges involved.

5. What are the applications of electrostatic pressure in science and technology?

Electrostatic pressure has various applications in science and technology, such as in particle accelerators, inkjet printers, electrostatic precipitators used to remove pollutants from air, and electrostatic motors. It is also essential in the study of plasma physics and plays a crucial role in the functioning of electronic devices like transistors and capacitors.

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